On a Higher-order System of Difference Equations

Here we study the following system of difference equations xn = f −1 ( cnf(xn−2k) an + bn ∏k i=1 g(yn−(2i−1))f(xn−2i) ) , yn = g −1 ( γng(yn−2k) αn + βn ∏k i=1 f(xn−(2i−1))g(yn−2i) ) , n ∈ N0, where f and g are increasing real functions such that f(0) = g(0) = 0, and coefficients an, bn, cn, αn, βn, γn, n ∈ N0, and initial values x−i, y−i, i ∈ {1, 2, . . . , 2k} are real numbers. We show that the system is solvable in closed form, and study asymptotic behavior of its solutions.